c

The Ion Acoustic Decay Instability, and Anomalous Laser Light Absorption for the OMEGA Upgrade, Large Scale Hot Plasma

-Application to a Critical Surface Diagnostic, and Instability at the Quarter Critical Density

by Katsu Mizuno, J. S. DeGroot

W. Seka, R. S. Craxton

R. P. Drake and K. Estabrook

Applied Science

Univ. of Calif. Davis

Final Report

for Contract DOE FG03-95SF20716

Phone (916) 752-0360 Phone (510) 422-6891 E-mail mizunol@LLNL.gov

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or use- fulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any spc- cific commercial product, process, or service by trade name, trademark, manufac- turer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

Table of Content

I. Introduction

II. Experimental Arrangement

III. Experiments

(a) Second Harmonic Spectrum

(b)

Anomalous Absorption of Laser Light

(a) Anomalous Collision Frequency

(b}

(c) Plasma Density Profile

(d)

Second Harmonic Emission vs Plasma Scale Length

IV.

Anomalous Attenuation of the Laser Light

Laser Light Attenuation Length, and Instability Width

(e) Two-Dimensional Electromagnetic Computer Simulation Results

V. Summary

References

3

5

6

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8

11

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13

14

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2

I. INTRODUCTION

The Ion Acoustic Parametric Decay Instability (IADI)1, in which an

electromagnetic wave decays into an electron plasma wave (epw) and an ion

acoustic wave (iaw) near the critical density nc (where the electromagnetic

wave frequency equals the plasma frequency), is a fundamentally important

subject in plasma physics. It has been studied by numerous authors in laser

plasma interaction$-3, microwave experiments$, and ionospheric studies.

One of the main issues of the IADI in laser produced plasmas is to understand

whether or not it is important in the large scale plasmas relevant to laser

fusion. The IADI is important because significant hot and/or warm electron

heating can occur even when it is relatively weak, if the unstable volume is

large enough3. If it is excited, it has important applications as plasma

diagnostic in addition to anomalous laser light absorption, hot and warm

electron heating, anomalous enhancement of lateral heat transport, and

anomalous DC resistivity.

When electromagnetic wave excites an epw, the energy is deposited in

hot/warm electrons. Previously, hot electron heating was calculated5 in a

plasma irradiated by a high intensity laser (IL2-lxlO15-lO18 W-p.m2/cm2). The

IADI was excited at a steep plasma. The plasma wave amplitude was large, and

the instability width was small. The self-consistent plasma density was steep,

and the instability was localized in a small region. Because of the strong

excitation of the epw, a significant amount of hot electrons was heated even in

the small heating region. It was thought relatively easy to avoid the hot

electron heating since a high intensity laser were needed to heat them. In

contrast, we find that the IADI threshold is quite low and reaches

homogeneous plasma collisional values in a laser produced large scale

3

plasma.3 Because of the weak laser intensity, the epw is excited only

moderately. However, the density profile modification is also weak, and the

plasma density gradient is gentle near the instability region, implying that the

instability width can be large. The electron heating is mostly determined by the

product of the plasma wave amplitude, and the instability width (of the

interaction time of the electron with the instability). For high intensity laser,

we have a large amplitude epw, and a small instability width. On the other

hand, for moderate intensity laser, we have a moderate amplitude epw, and a

large instability width. An important point is that a relatively weak instability

in a large region can heat (hot and warm) electrons as much as a strong

instability heats them in a small region. When the IADI is excited on a shallow

long scale length plasma, relatively low intensity laser can anomalously heat

electrons . f It is shown that laser light can be anomalously absorbed with a moderate

intensity laser (Ih2-1014 W/cm2-pm2). in a large scale, laser produced plasma.

The heating regime, which is characterized by a relatively weak instability in a

large region, is different from the regime studied previously, which is

characterized by a strong instability in a narrow region. The two dimensional

geometrical effect (lateral heating) has an important consequence on the

anomalous electron heating. The characteristics of the IADI, and the

anomalous absorption of the laser light were studied in a large scale, hot

plasma applicable to OMEGA upgrade plasma. These results are important for

the diagnostic application of the IADI.

4

11. EXPERIMENTAL

We made the simi

ARRANGEMENT

lation experiments 1 sing the Jan s Laser

facility, which is similar to GDL system at University of Rochester. The

experiments were made with a large scale length, hot plasma, which

simulated the IADI in OMEGA upgrade plasma. Laser wavelength h L =

1.06 pm and 0.53 pm, the laser pulse length ZL = 1.0 nsec, and the

maximum laser energy 200 J. The laser intensity IL was varied from

1012-3x1015 W/cm2 by controlling the laser energy, and the spot size

independently. The laser normally irradiates a planar CH target. The

laser light was focused through an f /2 lens onto the target. The target

was thick enough (50pm) that no burn through was observed. We

measured the emission spectrum near the second harmonic ( 2 0 ~ ) of the

incident laser, which was collected at 1350 and 1800 from the axis of the

incident laser, and in the plane of the laser electric field. A focusing lens

of 2 inches diameter were used to measure the emissions near the

second harmonic. The signal was fed through a optical fiber into a

spectrometer. The spectrum was streaked using a streak camera. The

typical spectral and time resolutions are 1 A, and 30 psec.

5

111. EXPERIMENTS

(a) Second Harmonic Spectrum

4000 , I I I 8 1 1 I I 1 1 I I I I I 1 8 1 1 I 1 I I I I I I I I , - - (61 - - - - - - 2000 : - - - -

FIGURE 1. Second harmonic spectrum: (A) IL = 3 x 1013 W/cm2, and (B)

2x1014 W/cm2.

We have measured emission spectrum near the second harmonic

of laser light in large scale, hot plasma. The IADI excites the epw and the

iaw, which satisfy the relation OL=Oepw + Stiaw, where oL, Qpw, and

Stiaw are the frequencies of the laser light, the epw, and the iaw. Two

electron plasma waves (oepw=oL-SLiaw and wepw'=oL-Qiawl) coupled to

produce an electromagnetic wave emission. The frequency is

approximately 2mppw = 20~-21(2iaw. In our previous paper, we reported

the IADI near the threshold, when it was excited weakly. When the

IADI is excited weakly near the threshold, we saw well defined Stokes

6

peaks. Figure 1 shows the second harmonic spectra for two laser

intensities; a weak intensity slightly above the IADI threshold, and a moderately high intensity. The left-hand peak is 202. signal which is

attributed to resonance absorption. The right-hand signal is a Stokes

signal emitted from the electron plasma waves excited by the IADI. A

sharp well-defined Stokes mode is excited with the weak intensity laser

irradiation (curve (a) in Fig. 1). The peak appears near the Landau

damping cutoff of the epw at kh& - 0.23. When the incident laser

intensity increases, the spectral shape is quite different from one shown

in curve (a). The spectrum becomes broad (curve (b) in Fig. l), and the

original Stokes peak is now barely distinguishable. In Fig. 1, the second

harmonic signals are plotted versus the measured wavelength Ah ( = h ~ -

h ). It is interesting to consider the horizontal axis as ~ P W . The Stokes

signal has a red shift by 2Qaw ( = 2kiawcs), where kiaw, and cs are the

wave number of the iaw, and sound speed. In our experiments, dipole

approximation is valid: 0 = kL = kepw + kiaw, or I kepw I = I kiaw I, where kL and kepw are the wave vectors of the laser light, and the epw.

The AA may be considered to be proportional to kepw when it is less than

the Landau damping cut off. Therefore, Fig. 1 indicates that the wave

number spectrum become broad as the laser intensity increases. The

spectral intensity was large at small k p w , and gradually decreased with

the increasing kepw. The measured spectrum is the results of the signals

integrated over the plasma density (0.8 w-nc), and the propagation angle

of the epw.

The spectral broadening of the Stokes mode is of interest. It may

be relevant to the degree of turbulence of the epw. In order to quantify

the broadening, we introduce a following definition. We define the peak

7

intensity of the Stokes mode as Imax, and the minimum intensity

between 2 o ~ and the Stokes peak as Imin. We can then quantify the

broadness of the Stokes mode using the value Imin/Imax. If it is nearly

one (or small), the spectrum is almost flat (or sharp). When laser

intensity was less than 2x1013 W/cm2, the Imin/Imax increased strongly

with the laser intensity. Above the laser intensity, the Imin/Imax

reached a value nearly equal to unity with Only moderately high laser

intensity. The spectrum was built up at smaller kepw to make a

uniform spectrum. It is also interesting to note that the peak value of

the Stokes mode moved towards smaller kepw as laser intensity

increased. The spectral intensity gradually decreases with the measured

wavelength ( or ~ P W ) as shown in Fig. 1 (b). The epw's with smaller

kepw interact with higher energy electrons because they have higher

phase velocities. These small kepw's could be either produced by the

mode couplings of the plasma waves (turbulent like spectrum) or excited

by the IADI at higher density.

(B) Second Harmonic Emission versus Plasma Scale Length

As shown in the previous pape3, the IADI shifted from

convective-loss regime to uniform plasma regime when laser spot size

increased. The IADI can be excited in a large volume. Hence , we expect

to see the increase of the IADI emissions. We have seen that the Stokes

intensity increases with the laser spot size. For the small spot of the

diameter D=100 p m, no Stokes spectrum was seen because the laser

intensity is lower than the IADI threshold (Notice that the IADI

threshold increased with the decreasing laser spot size). Only 2 0 , signal

8

is detected. When the laser spot size is large enough that the laser

intensity is above the IADI threshold values, the Stokes signal increased

with D. In order to keep the laser intensity constant, we increased the

total incident laser energy with increasing D. Therefor, we have

measured the normalized Stokes intensity ISto/n: (D/2)2, the Stokes

intensity divided by the laser spot area. The normalized Stokes signal

increased with the laser spot diameter D.

Although, we did not rule out other possible explanations, these

results may imply that the instability width LIADI increased (because the

plasma scale length increased) with D, so the measured Stokes intensity

(which is integrated over space in the instability width LIADI) increased.

The Instability width LIADI is an important parameter to determine the

anomalous laser absorption as is shown in the following sections,.

The IADI causes anomalous absorption of laser. It is shown in the

following chapter that the anomalous attenuation length of laser can be

shorter than the IADI instability width in a large scale length plasma.

Then, most of the laser energy will be absorbed by the IADI before it

reaches the critical surface. Therefore, resonance absorption which

happens close to the critical surface should be less important in a large

scale plasma.

We have measured the intensity ratio of Stokes mode to 200

signal vs laser spot diameter. The intensity ratio increased with the spot

diameter. The Stokes intensity increased much faster than 200 intensity

with the spot diameter. The value decreased strongly with laser spot

size. Notice that no IADI was excited with the laser spot diameter of 100

pm. The results are qualitatively consistent with the large scale plasma

9

where the laser energy is absorbed anomalously by the IADI before it

reaches the critical density.

The large reduction of the resonance absorption with plasma scale

length should not be attributed to the nature of characteristic resonance

function of resonance absorption. The fractional absorption of laser fA

by resonance absorption1 is approximately given by 92(2)/2, where $(z) =

2.3 z exp (-2z3/3) is the characteristic resonance function describing the

strength of the excitation, and z = (o~/c)l/%ine. The L is plasma scale

length, 8 is the incident angle of laser, and c is speed of light. The

optimum resonance absorption happens at z = 0.8. In our experiments,

laser is normally incident onto plasma through an f/2 lens. Hence the

maximum incident angle of laser is 140. The fractional absorption fA is

estimated versus plasma scale length L for the incident laser angles of

140, 70, and 3.50 using our experimental parameters. The optimum

absorption just shifts from large to small angles, as the value of L

increases. Therefore, we don't expect a strong reduction of the resonance

absorption as L increases, from the nature of the characteristic resonance

function.

10

IV. ANOMALOUS ABSORPTION OF LASER LIGHT

2 -= 10 a L 0.56 v* 4.1~10- x(-) cy_ Te

(a) Anomalous Collision Frequency Estimated from One-Dimensional

Particle in Cell (PIC) Computer Simulation

An important parameter to characterize anomalous absorption of laser light

is anomalous collision frequency v*. The anomalous collision frequency is the

heating rate of electrons by electron plasma wave. We have the definition of

the anomalous collision frequency.

We estimated the v* by measuring the temporal increase of the total plasma

energy density, dT/dt, using one dimensional electrostatic PIC computer

simulation code, where EL is laser electric field. Figure 2 shows the v* vs the

local laser intensity I (laser intensity at 0.9 nc) for a fixed plasma density, n/nc

0.9, which is the mid point between 0.8 nc, and nc, and it is slightly above the

0.86 nc, where the IADI is most unstable. We plotted the v* versus the

normalized laser intensity IhL’/Te. The swelling effect of the laser light was

included. The v* increases with IhL2/Te until the shifting point intensity of

3x1014 W-pm2/cm2keV, and above the intensity v* increases slowly. In the

moderate (laser) intensity regime below the shifting point, the anomalous

collision frequency scales as

11

0.1 I I

ox /a L

J 0.0 1 I I

1 0lS 1 014 1 0lS 1 o le

lh,2/T (Wpm2/cm2 key)

FIGURE 2. Anomalous collision frequency vs. the normalized laser intensity

IkL’/Te (W-pm2/cm2keV) obtained from one dimensional particle

simulations.

(b) Anomalous attenuation of the laser light

The transfer of energy from laser to electrons via the IADI (the rate of

energy loss from laser light) is given by u * E ~ 2 / 8 n . When we consider the

spatial problem, the (e-folding) attenuation length of laser energy 6 is given by

vg/u* in term of the group velocity vg of laser light in plasma. Therefore we

have

, which depends strongly on the anomalous collision frequency v*. In deriving

the equation (3), the group velocity of the laser light is assumed to be 0.37~ (c is

12

the speed of light), which is estimated at a plasma density n/nc = 0.86, where

the IADI linear growth rate has a peak value.

By combining Eqs. (Z), and (3), we can estimate the laser attenuation

length due to the IADI as

2 6 8 ILL -0.56 - 1.5~10 x(-) LL Te

For a simple estimate, we ignore the plasma density dependence of 'u *. This

simple approximation will be justified, since 6 <<LIADI as is discussed in the

following section. The accurate value depends on the detail of the density

profile, and local value of v*. The important point is that our simple estimates

indicate that the attenuation length of the laser can be much smaller than the

instability width as shown in the following section.

(c) Plasma Density Profile

We have made computer calculations of the plasma density profile using

the 2-dimensional LASNEX computer codeb. The calculations were made

using our experimental parameters: the 1.06 pm laser, with 1 nsec Gaussian

pulse, was focused onto a 50 pm thick planar CH target using f/2 lens (the laser

spot size was 500 pm). The laser intensity was 3x1013, and 1014 W/cm2, and

the flux limiter was f = 0.1.

The plasma scale length was long near the instability region. The

electron temperature was about 0.7 keV. It is well known that the IADI can be

excited3 at the densities 0.8 < n/nc 1. The lower limit density is determined

13

by the Landau damping cut off of the epw near the kepwkDe = 0.3 (kepw, and

hDe are wave number of the epw, and Debye length). Let's define the length

between nc and 0.8 nc as the instability width, LIADI. For the above

parameters, the length LIADI was quite large, about 30 ym for the both laser

intensities of 3x1013, and W/cmz.

(d) Laser Light Attenuation Length, and the Instability Width

We can now compare the laser attenuation length and the instability

width. For laser intensity 3x1013 W/cm2(1014), the electron temperature is

about 0.7 keV (l), so we have 6 / h ~ - 3 (2) using Eq. (4). On the other hand,

L I A D I / ~ L - 30 for the both laser intensities. The attenuation length is much

smaller than the instability width. Therefore, we predict without the accurate

spatial profile of v* that the most laser energy which reaches the instability

region is absorbed by the IADI. The absorbed energy is deposited to hot and

warm electrons.

(e) Two-Dimensional Electromagnetic Computer Simulation Results

These results are consistent with the calculations using the two-

dimensional relativistic particle and electromagnetic field simulation code

ZOHAR7. Figure 2 shows laser absorption versus LIADI. It shows that the

instability width LIADI of only a few laser wavelengths may be sufficient to

absorb most of laser energy. The ZOHAR simulations were made with high

laser intensities to minimize the numerical noise. However, v* saturates at

high laser intensity as shown in Fig. 2, sc that the results should be insensitive

to the laser intensity. In fact, when we increased the laser intensity from 5x1015

14

to lx1016W/cm2, no significant change of the absorption was seen. For

comparison, we plotted the theoretical values calculated using the v* given in

Fig. 2. The simple estimates give reasonably good agreements with ZOHAR

results. The important point is that there was no drastic change of the

anomalous absorption as laser intensity increased from 1014 to 5x1015 W/cm2.

100

80

60

4 0

20

0 0.1 10

FIGURE 3. The solid circles are fraction of laser absorption calculated by

ZOHAR simulations. The curves are the theoretical values for (a) : 5x1015

W/cm2 and 4 keV, and (b): I = 1014 W/cm2, and Te = 1 keV.

15

V. SUMMARY

3.

5.

6.

7.

In summary, anomalous absorption in a large scale plasma is quite

different from those of small scale plasmas. The Ion Acoustic Decay Instability

(IADI) may cause anomalous laser absorption with a relatively weak laser

intensity in a large scale plasma. The anomalous attenuation length of the

laser can be only a few laser wavelengths in width. These are consistent with

the 2-dimensional electromagnetic field computer simulation results. The

experiments indicate that the threshold of the IADI is low, so that the IADI is

excited on a shallow, long scale length plasma. The measured results of the

second harmonic signals are consistent with a strong anomalous absorption by

the IADI in a large scale plasma.

REFERENCES

1.

2.

W. L. Kruer, The Physics of Laser Plasma Interactions (Addition-Wesley, Reading, MA,

1988); K. Nishikawa, J Phys. Soc. Jpn. 24,916, and 1152 (1968).

C. Yamanaka et al, Phys. Rev. Lett. 30,594 (1973); K. Tanaka et al, Phys. Fluids 27, 2187

(1984); F. Dahmani et al, Phys. Fluids B3, 2558 (1991).

K. Mizuno et al, Phys. Rev. Lett. 65, 428 (1990); K. Mizuno et al, Phys. Fluids B 3, 1983

(1991); K. Mizuno et al, Phys. Rev. Lett. 73,2704 (1994).

K. Mizuno et al, Phys. Rev. Lett. 52, 271 (1984); K. Mizuno et al, Phys. Rev. Lett. 56,2184

(1986).

K. Estabrook, and W. L. Kruer, Phys. Fluids 26,1888 (1983).

G. B. Zimerman and W. L. Kruer, Comments Plasma Phys. Controlled Fusion 2/51 (1975).

A. B. Langdon, and B. F. Lasinski, In Methods in Computational Physics, edited by J.

Killeen (Academic, New York, 1976), Vol. 16, p327.

4.

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